self-aligned double patterning layout decomposition with ...byu/papers/...sadpebl-slides.pdf ·...
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Self-aligned Double Patterning Layout Decomposition with
Complementary E-Beam Lithography
Jhih-Rong Gao, Bei Yu and David Z. Pan Dept. of Electrical and Computer Engineering
The University of Texas at Austin
Supported in part by NSF, SRC, NSFC, IBM and Intel
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Outline
t Motivation & Problem Formulation t Proposed Algorithms
› Post Processing Based Layout Decomposition › Simultaneous SADP+EBL Optimization
t Experimental Results t Conclusion
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Self-Aligned Double Patterning (SADP) t Promising double patterning technique for sub-22nm nodes t Trim mask can be used to generate cuts t Issue: Overlay problem caused on some trimming boundaries
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Target layout Mandrel mask Spacer deposition Trimming Assist
Trim mask
Possible overlay error
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E-Beam Lithography (EBL)
t Maskless lithography › High Resolution (sub-10nm)
t Issue: Low throughput t Constraint: Variable-shaped (rectangular) beam
system › Each e-beam cut is a rectangular
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Electrical Gun
Shaping Aperture
2nd Aperture
Wafer
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SADP & E-beam Hybrid?
t SADP with multiple cut masks or e-beam cuts
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4442010 Int’l Symposium on Litho Extensions2010 Int’l Symposium on Litho Extensions
•• Borodovsky (Intel) shows 193 nm immersion (193i) requires Borodovsky (Intel) shows 193 nm immersion (193i) requires 5 masks for 11 nm Node (40nm pitch) HVM in 2015: 5 masks for 11 nm Node (40nm pitch) HVM in 2015:
! 1 to create the lines and 4 to break continuity (“cut” lines)
Industry Trend # 2: Complementary LithoIndustry Trend # 2: Complementary Litho
–– Borodovsky, Y. (Maskless Litho and Multibeam Mask Workshop 2010Borodovsky, Y. (Maskless Litho and Multibeam Mask Workshop 2010))
Mask Count:12345
[Y. Borodovsky, Maskless Lito and Multibeam Mask Workshop, 2010 ]
193nm immersion Complementary Lithography 1 base mask + 4 cut masks 1 base mask + E-beam
11nm node
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Complementary/Hybrid Lithography
t Different lithography techniques work together › Base features: Optical lithography or SADP
» Low cost, low resolution › Cutting technique: high-resolution MPL/EUVL/EBL/DSA
» High cost, high resolution
› Tradeoff b/t Printing Quality and Manufacturing Cost t This work: SADP + EBL
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+ =
Base features
Cutting patterns
Final patterns
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Related Works
t Complementary lithography › [Y. Borodovsky, Maskless Lithography and Multibeam
Mask Writer Workshop, 2010] t SADP with line cutting for 1D layout
› [K. Oyama et al., SPIE 2010] t SADP with EBL line cutting for 1D layout
› [D. Lam et al., SPIE 2011], [Y. Du et al., ASPDAC 2012]
t SADP layout decompositions for 2D layouts › [Ban+, DAC’11], [H. Zhang+, DAC’11 ], [Xiao+, TCAD
13]
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Problem Formulation
t Given › General 2D layouts › Minimum pattern spacing on a single mask
t Objective: Perform layout decomposition with SADP+EBL
› No min-spacing conflict for mandrel/trim mask › Minimize overlay error caused by trim mask › Minimize e-beam shots
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Outline
t Motivation & Problem Formulation t Proposed Algorithms
› Post Processing Based Layout Decomposition › Simultaneous SADP+EBL Optimization
t Experimental Results t Conclusion
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Dealing with SADP Conflicts
t Merge&Cut (M&C) technique › Step1: Merge conflicting patterns › Step2: Cut unwanted parts by trim mask or e-beams
conflicts
Non-SADP- decomposable
Cut
+
Trim mask or E-beam
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Merge
SADP- decomposable
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Merge & Cut (M&C) Technique t May have multiple solution candidates t Cut cost
› Cost of trim mask cut = α * Length of cutting boundary » Penalty to minimize overlay error
› Cost of e-beam cut = β * Number of shots required » Set β much larger than α to minimize e-beam shot counts
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cut3
cut1
cut2
assist
conflicts Mandrel mask
Formed by aligning to spacers
Solution 1
Solution 2 Trim mask
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t Objective: solve all conflicts with minimum cost t Matching-based algorithm
› Step1: Conflict Graph construction › Step2: Dual Face Graph construction
» Conflict node: an odd face on the conflict graph » M&C node: a M&C candidate to solve a conflict » Edge: b/t a conflict node and its M&C solution candidates
Finding M&C Solutions
12 Face graph Conflict graph
Conflict Odd cycle = Conflict
Merge&cut candidate
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t Matching-based algorithm › Step 3: Apply min-cost matching algorithm on face graph
» Edge = conflict solved by a M&C candidate » Each conflict node only needs to be covered once
èMatching solution = Selection of M&C candidates that can solve conflicts with the minimum cost
Finding M&C Solutions (cont)
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cut3
cut1
cut2
assist
Matching 1
Matching 2
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Method 1: Post Processing Based Layout Decomposition
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• Min-Cost Matching Algorithm • Assign all M&C candidates with the
cost of trim mask cuts
SADP Mask + EBL Assignment
cut5 cut6
Cuts obtained may conflict each other
New Conflict
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Method 1: Post Processing Based Layout Decomposition (cont)
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• Construct conflict graph for cuts • Find trim cuts by Maximal
Independent Set algorithm • Assign the rest of cuts as e-beams
E-beam only considered at the last stage (Greedy)
SADP Mask + EBL Assignment
E-beam cuts
Trim cuts
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Method 2: Simultaneous SADP+EBL Optimization
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SADP Mask + EBL Assignment
Min-Cost Matching Algorithm
Start From Restricted Solution Space • Assign all M&C candidates with
the cost of trim mask cuts
Gradually Increase Solution Space • Replace conflicting trim mask cuts
as e-beam cuts
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Method 2: Simultaneous SADP+EBL Optimization (cont)
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SADP Mask + EBL Assignment
Min-Cost Matching Algorithm • Similar to the previous
iteration, but now we have two types of cuts
• E-beam Cut Cost >> Trim Cut Cost
Simultaneously selecting trim mask cuts and e-beam cuts
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Example of SADP+EBL Optimization
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1 1
1 1 1
2 1
Iter. 1 Matching solution
cut
cut
Conflict
Check trim cuts
t Initialize cost of all cuts based on trim mask cutting length
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Example of SADP+EBL Optimization
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1 1
1 1 β
2 1
Iter. 2 Matching solution
cut Conflict
Check trim cuts
cut
t Update one conflicting cut as EBL cut (cost = β)
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Example of SADP+EBL Optimization
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β
1
1 1 β
2 1
Iter. 3 Matching solution
cut
Conflict
Check trim cuts
cut
t Update cost
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Example of SADP+EBL Optimization
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β
β
1 1 β
2 1
β
Keep going…
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Example of SADP+EBL Optimization
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β β
1 1 β
β 1
Final matching solution Final cut assignment
EBL cut
Trim cut
t Continue iterations until no conflict in cuts
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Experiment Settings
t Benchmarks › OpenSPARC T1 designs › Scaled down to 22nm
t Comparison methods › SADP w/o merge&cut › SADP w/ merge&cut › Hybrid-post: post-processing based decomposition › Hybrid-sim: simultaneous SADP+EBL decomposition
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Comparison of Remaining Conflicts
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All conflicts are solved with hybrid lithography
#Conflict
Design
≈
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Comparison of E-beam Utilization
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#E-beams
Design Hybrid-sim tends to use more trim mask cutting and less e-beams
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Comparison of Overlay Error
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Overlay Error (um)
Design
Overlay increase by Hybrid-sim < 3%
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Conclusion
t Complementary lithography enables high quality layout with less mask manufacturing cost
t Merge & cut technique to reduces conflicts t Simultaneous SADP layout decomposition and
E-beam assignment performed effectively to minimize
› Conflict › SADP overlay due to trim mask › E-beam shot counts
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Thank You
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